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Water and Ice Dielectric Spectra Scaling at 0 °C

Dielectric spectra (10^4-10^11 Hz) of water and ice at 0 °C are considered in terms of proton conductivity and compared to each other. In this picture, the Debye relaxations, centered at 1/τ_W ~ 20 GHz (in water) and 1/τ_I ~ 5 kHz (in ice), are seen as manifestations of diffusion of separated charges in the form of H3O+ and OH- ions. The charge separation results from the self-dissociation of H2O molecules, and is accompanied by recombination in order to maintain the equilibrium concentration, N. The charge recombination is a diffusion-controlled process with characteristic lifetimes of τ_W and τ_I, for water and ice respectively. The static permittivity, ε(0), is solely determined by N. Both, N and ε(0), are roughly constant at the water-ice phase transition, and both increase, due to a slowing down of the diffusion rate, as the temperature is lowered. The transformation of the broadband dielectric spectra at 0 °C with the drastic change from τ_W to τ_I is mainly due to an abrupt (by 0.4 eV) change of the activation energy of the charge diffusion.